Minimum Size Subarray Sum

Problem

Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.

Examples

The brute-force approach

Try every possible subarray. For each starting index, extend the subarray one element at a time until the sum reaches the target. Track the shortest such subarray found.

min_len = float('inf')

for i in range(len(nums)):
    total = 0
    for j in range(i, len(nums)):    # extend right
        total += nums[j]
        if total >= target:
            min_len = min(min_len, j - i + 1)
            break    # no need to go longer from this start

return 0 if min_len == float('inf') else min_len

You're recomputing sums starting from every index, which is O(n²). The key insight: all values are positive, so once a window's sum is large enough, shrinking it from the left is the only way to find something shorter. A sliding window handles that in one pass.

Spotting the pattern

This is a Sliding Window problem. The key question to ask yourself:

Once my running sum hits the target, how do I know if I can shrink the window and still meet the condition?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.